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C ================================================================
Subroutine Delaunay(
C ================================================================
& nP, nE, XYP, IPE,
& MaxWr, MaxWi, rW, iW)
C ================================================================
implicit none
include 'makS.fd'
C ================================================================
C The routine builds the Delaunay triangulation from the existing
C triangution by swapping edges in pairs of triangles.
C
C Data flow:
C 1. calculate map E->E
C 2. loop over triangles
C 2.1 check criterium for sum of opposite angles
C 2.2 swap triangles
C 2.3 update the map
C
C *** Remarks
C ================================================================
Integer nP, nE
real XYP(2, *)
Integer IPE(3, *)
Integer MaxWr, MaxWi, iW(*)
real rW(*)
Integer iref(4)
Logical check22, DelonePair, flagREPEAT, flagDELONE
Integer i1,i2,i3, j1,j2,j3, k, n
Integer iP1,iP2,iP3, jP1,jP2,jP3, iE1,iE2, jE2,jE3
Integer inEp, iIEP, iIEE, iEnd, iEmem, jEmem, kEmem
Integer nswap, nswapold, nloop
real sa1, sa2
DATA iref /1,2,3,1/
C ================================================================
iIEE = 1
inEP = iIEE + 3 * nE
iIEP = inEP + nP
iEnd = iIEP + 3 * nE
If(iEnd.GT.MaxWi) Call errMes(1001,
& 'delaunay', 'MaxWi is too small')
Call listE2E(nP, nE, IPE, iW(iIEE), iW(inEP), iw(iIEP))
c ... initialize loops
nswapold = nE
nloop = 0
c ... new loop
100 flagREPEAT = .FALSE.
nswap = 0
Do n = 1, nE
Do 30 i1 = 1, 3
iEmem = iIEE + 3 * (n - 1) - 1
iE1 = iW(iEmem + i1)
If(iE1.LE.n) goto 30
i2 = iref(i1 + 1)
i3 = iref(i2 + 1)
iP1 = IPE(i1, n)
iP2 = IPE(i2, n)
iP3 = IPE(i3, n)
Do j1 = 1, 3
j2 = iref(j1 + 1)
jP1 = IPE(j1, iE1)
jP2 = IPE(j2, iE1)
If(check22(iP1, iP2, jP1, jP2)) Then
j3 = iref(j2 + 1)
jP3 = IPE(j3, iE1)
goto 10
End if
End do
10 Continue
flagDELONE = DelonePair(XYP(1, iP1), XYP(1, iP2),
& XYP(1, iP3), XYP(1, jP3), sa1)
If(.NOT.flagDELONE) Then
flagREPEAT = .TRUE.
flagDELONE = DelonePair(XYP(1, iP3), XYP(1, jP3),
& XYP(1, iP1), XYP(1, jP2), sa2)
If(flagDELONE .OR. sa2.GT.sa1) Then
nswap = nswap + 1
iE2 = iW(iEmem + i2)
jEmem = iIEE + 3 * (iE1 - 1) - 1
jE2 = iW(jEmem + j2)
jE3 = iW(jEmem + j3)
If(iP1.NE.jP1) Call swapii(jE3, jE2)
IPE(i1, n) = iP3
IPE(i2, n) = jP3
IPE(i3, n) = iP1
IPE(j1, iE1) = iP3
IPE(j2, iE1) = jP3
IPE(j3, iE1) = iP2
iW(iEmem + i2) = jE3
If(jE3.GT.0) Then
kEmem = iIEE + 3 * (jE3 - 1) - 1
Do k = 1, 3
If(iW(kEmem + k).EQ.iE1) Then
iW(kEmem + k) = n
goto 20
End if
End do
c Call draw_T(nP, 0, nE, XYP, iW, iW, IPE, 'fin.ps')
Call errMes(6006,
& 'delaunay.f', 'Cannot build Delaunay mesh')
End if
20 iW(jEmem + j2) = jE2
iW(jEmem + j3) = iE2
If(iE2.GT.0) Then
kEmem = iIEE + 3 * (iE2 - 1) - 1
Do k = 1, 3
If(iW(kEmem + k).EQ.n) Then
iW(kEmem + k) = iE1
goto 30
End if
End do
c Call draw_T(nP, 0, nE, XYP, iW, iW, IPE, 'fin.ps')
Call errMes(6006,
& 'delaunay.f', 'Cannot build Delaunay mesh')
End if
End if
End if
30 Continue
End do
If(flagREPEAT) Then
nloop = nloop + 1
If(nloop.GT.nE) Then
c Call draw_T(nP, 0, nE, XYP, iW, iW, IPE, 'fin.ps')
Call wrnMes(6006,
& 'delaunay.f', 'Cannot build Delaunay mesh')
Return
End if
nswapold = nswap
goto 100
End if
Return
End
C ================================================================
Logical Function DelonePair(xy1, xy2, xy3, xy4, sa)
C ================================================================
C This roune checks that the pair {1,2,3} and {1,2,4} is the
C Delaunay pair. It returns .FALSE.otherwise.
C ================================================================
real xy1(2), xy2(2), xy3(2), xy4(2)
real sa, sb, ca, cb
C ================================================================
DelonePair = .FALSE.
ca = 0
cb = 0
Do i = 1, 2
ca = ca + (xy4(i) - xy1(i)) * (xy4(i) - xy2(i))
cb = cb + (xy3(i) - xy1(i)) * (xy3(i) - xy2(i))
End do
c ... Delaunay condition fails
If(ca.LT.0 .AND. cb.LT.0) goto 9000
c ... Delaunay condition true
If(ca.GE.0 .AND. cb.GE.0) Then
DelonePair = .TRUE.
goto 9000
End if
c ... the rest of the formula
sa = (xy4(1) - xy1(1)) * (xy4(2) - xy2(2))
& - (xy4(1) - xy2(1)) * (xy4(2) - xy1(2))
sb = (xy3(1) - xy1(1)) * (xy3(2) - xy2(2))
& - (xy3(1) - xy2(1)) * (xy3(2) - xy1(2))
c ... checking when swapping is not possible
c If(sa * sb.GE.0) goto 9000
sa = abs(sa) * cb + ca * abs(sb)
If(sa.GE.0) DelonePair = .TRUE.
9000 Return
End
C ==============================================================
Subroutine RandXY(xy1, xy2, xy3, xyc, r)
C ==============================================================
C Routine computes the center and radius of the circle
c curcumscribed around triangle defined by three vertices.
C ==============================================================
real xy1(2), xy2(2), xy3(2)
real xyc(2), r
real a, b, c, x1, y1, x2, y2, r1, r2
C ==============================================================
x1 = xy1(1) - xy3(1)
y1 = xy1(2) - xy3(2)
x2 = xy2(1) - xy3(1)
y2 = xy2(2) - xy3(2)
r1 = x1 ** 2 + y1 ** 2
r2 = x2 ** 2 + y2 ** 2
a = x1 * y2 - y1 * x2
b = r1 * y2 - r2 * y1
c = r1 * x2 - r2 * x1
xyc(1) = b / (2 * a)
xyc(2) =-c / (2 * a)
r = sqrt(xyc(1) ** 2 + xyc(2) ** 2)
xyc(1) = xyc(1) + xy3(1)
xyc(2) = xyc(2) + xy3(2)
Return
End
C ==========================================================
Subroutine draw_D(nP, nF, nE, XYP, ICP, IPF, IPE, fName)
C ==========================================================
include 'colors.fd'
C ==========================================================
C Routine converts the Delaunay mesh into a postcript file fName.
C ==========================================================
C group (M)
real XYP(2, *)
Integer ICP(*), IPF(4, *), IPE(3, *)
C group (File)
Character*(*) fName
C group (Local variables)
Real mmTOpt, kx, ky
Real x1, y1, x2, y2, x3, y3
Real fxmax, fymax
real calEdge
Logical ifXnode
real xyc(2), rOut, rad
Character*30 fNameExt
C ==========================================================
i = 1
Do while( fName(i:i+2) .NE. '.ps')
i = i + 1
End do
fNameExt = fName(1:i+2)
mmTOpt = 72.0 / 25.4
Pi = 4.0*atan(1.0)
rdTOdg = 180.0 / Pi
xBig = 150.0
yBig = 150.0
fxmax = XYP(1, 1)
fxmin = fxmax
fymax = XYP(2, 1)
fymin = fymax
Do n = 2, nP
fxmin = min(fxmin, real(XYP(1, n)))
fxmax = max(fxmax, real(XYP(1, n)))
fymin = min(fymin, real(XYP(2, n)))
fymax = max(fymax, real(XYP(2, n)))
End do
kx = xBig / (fxmax-fxmin) * mmTOpt
ky = yBig / (fymax-fymin) * mmTOpt
If(kx.GT.ky) kx = ky
ibx = (fxmax-fxmin) * kx + 10
iby = (fymax-fymin) * kx + 10
Open(30, file = fNameExt, status='UNKNOWN')
Call headerPS(30, ibx, iby)
Do n = 1, nP
x1 = (XYP(1, n) - fxmin) * kx
y1 = (XYP(2, n) - fymin) * kx
c Write(30,*) x1,y1, ' m', x1, y1, n, ' intTOtext ctext'
End do
Do 10 n = 1, nE
If(IPE(1, n).EQ.0) goto 10
x1 = (XYP(1, IPE(1, n)) - fxmin) * kx
y1 = (XYP(2, IPE(1, n)) - fymin) * kx
x2 = (XYP(1, IPE(2, n)) - fxmin) * kx
y2 = (XYP(2, IPE(2, n)) - fymin) * kx
x3 = (XYP(1, IPE(3, n)) - fxmin) * kx
y3 = (XYP(2, IPE(3, n)) - fymin) * kx
Write(30,*) 'newpath'
Write(30,*) x1,y1, ' m', x2,y2, ' l', x3,y3, ' l'
Write(30,'(A)') ' closepath cBlack stroke'
c ... mark fix points
rad = fxmax - fxmin
Do i = 1, 3
iP1 = IPE(i, n)
Do j = i + 1, 3
iP2 = IPE(j, n)
rad = min(rad, calEdge(XYP(1, iP1), XYP(1, iP2)))
End do
End do
rad = rad * kx / 4
rad = min(rad, 1D0)
Do i = 1, 3
iP1 = IPE(i, n)
If(ifXnode(ICP(iP1), jVnode)) Then
x1 = (XYP(1, iP1) - fxmin) * kx
y1 = (XYP(2, iP1) - fymin) * kx
Write(30,*) x1,y1, rad, ' cRed fillCircle'
End if
End do
10 Continue
c ... draw boundaries using thick lines
Do 20 n = 1, nF
If(IPF(1, n).LE.0) goto 20
iP1 = IPF(1, n)
iP2 = IPF(2, n)
x1 = (XYP(1, iP1) - fxmin) * kx
y1 = (XYP(2, iP1) - fymin) * kx
x2 = (XYP(1, iP2) - fxmin) * kx
y2 = (XYP(2, iP2) - fymin) * kx
Write(30,*) x1,y1, ' m', x2,y2, ' l '
c Write(30,*) x1,y1, x2,y2, ' emptyArrow '
ic = IPF(4, n) / 5
ic = max(0, IPF(4, n) - 5 * ic)
Write(30,'(A,I1,A)') 'c', ic, ' stroke'
x1 = (x1 + x2) / 2
y1 = (y1 + y2) / 2
c Write(30,*) x1,y1, ' m', x1, y1, n, ' intTOtext ctext'
20 Continue
c ... draw the circumcribed circle
Do 30 n = 1, nE
If(IPE(1, n).EQ.0) goto 30
iP1 = IPE(1, n)
iP2 = IPE(2, n)
iP3 = IPE(3, n)
Call RandXY(XYP(1, iP1), XYP(1, iP2), XYP(1, iP3), xyc, rOut)
x1 = (xyc(1) - fxmin) * kx
y1 = (xyc(2) - fymin) * kx
rad = rOut * kx
Write(30,*) ' gsave', x1, y1,
& ' translate newpath 0 0 ', rad,
& ' 0 360 arc closepath cGray stroke grestore'
30 Continue
Write(30,'(A)') 'showpage '
Close(30)
Return
End
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